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Essentially commutative C*-algebras with essential spectrum homeomorphic to S2n−1
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 70 / Issue 2 / April 2001
- Published online by Cambridge University Press:
- 09 April 2009, pp. 199-210
- Print publication:
- April 2001
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- Article
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This paper gives a complete classification of essentially commutative C*-algebras whose essential spectrum is homeomorphic to S2n−1 by their characteristic numbers. Let
1, 2 be such two C*-algebras; then they are C*-isomorphic if and only if they have the same n-th characteristic number. Furthermore, let γn() = m then is C*-isomorphic to C*(Mzl, …, Mzn) if m = 0, is C*-isomorphic C*(Tz1, …, Tzn−1, Tznm) if m ≠ 0. Some examples are given to show applications of the classfication theorem. We finally remark that the proof of the theorem depends on a construction of a complete system of representatives of Ext(S2n−1).
